pair of st line

This is a set of 3 lines passing through the origin..

Now you should take y/x as m

then it will be a cubic in m
dm³+cm²+bm+a = 0

Now try and make it better by saying that 2 of the roots of the cubic equation in m are such that m1m2=-1

m1m2m3= -a/d

m1m2+m1m3+m2m3=b/d

m1+m2+m3 = -c/d

using m1m2 = -1, we can reduce the above equations to

m3 = a/d
(m1+m2)m3 = b/d+1

(m1+m2)+m3 = -c/d

again using the value of m3 as a/d in the remainaing 2 equations, we get

m1+m2 = (d/a)(b/d+1)

and (m1+m2) = -c/d-a/d

hence we have -c/d-a/d = (d/a)(b/d+1)

-c/d-a/d = (d/a)(b+d)/d

so -c-a = d/a(b+d)

so -ac-a² = db+d²

so db+d²+ac+a² = 0